Properties of Quadrilaterals

Parallelograms have two pairs of parallel sides. This means that I need to look for what kind of angles?

- alternate interior angles (because they are congruent) - same-side interior angles (because they are supplementary)

Name all of the quadrilaterals that have 2 pairs of congruent base angles.

- isosceles trapezoid

Name all the quadrilaterals with congruent diagonals.

- isosceles trapezoid - rectangle - square

Name all the quadrilaterals with perpendicular diagonals.

- kite - rhombus - square

Name all the quadrilaterals in which both diagonals bisect each other.

- parallelogram - rectangle - rhombus - square

Name all the quadrilaterals that have two pairs of opposite congruent sides.

- parallelogram - rectangle - rhombus - square

Name all the quadrilaterals with two pairs of opposite congruent angles.

- parallelogram - rectangle - rhombus - square

Name all the quadrilaterals that that have any same-side interior angles that are supplementary.

- parallelogram - rectangle - rhombus - square - trapezoid - isosceles trapezoid

Name all the quadrilaterals in which the diagonals form 4 isosceles triangles.

- rectangle - square

Name all of the quadrilaterals in which both diagonals bisect the angles (that they intersect).

- rhombus - square

What is it called when a rectangle has all the properties of a rhombus?

A square. A square is a rectangle with 4 congruent sides.

What is it called when a rhombus has all the properties of a rectangle.

A square. A square is a rhombus with 4 right angles.

If two angles are supplementary, what should you do?

Add them together and set them equal to 180 degrees. Then solve, if needed.

What are the properties of an isosceles trapezoid?

IT1)- one pair of congruent legs IT2) two pairs of congruent base angles IT3) diagonals are congruent Because an isosceles trapezoid is a trapezoid: T1) exactly one pair of parallel sides T2) same-side interior angles on the same leg are supplementary T3) bases are parallel Because an isosceles trapezoid is a quadrilateral: Q1) angles sum to 360 degrees

What are the properties of a kite?

K1) no parallel sides (2 pairs of adjacent, congruent sides) K2) perpendicular diagonals K3) one diagonal bisects exactly one pair of opposite angles K4) exactly one pair of opposite angles are congruent K5) the longer diagonal bisects the shorter one Because a kite is a quadrilateral: Q1) angles sum to 360 degrees

What are the properties of a parallelogram?

P1) exactly two pairs of parallel sides P2) opposite sides are parallel P3) opposite sides are congruent P4) both pairs of opposite angles are congruent P5) same-side interior angles are supplementary P6) diagonals bisect each other Because a parallelogram is a quadrilateral: Q1) angles sum to 360 degrees

What are the properties of a quadrilateral?

Q1) angles sum to 360 degrees Remember, a quadrilateral has 4 sides and 4 angles!

What are the properties of a rectangle?

RE1) all angles are right angles RE2) diagonals are congruent RE3) diagonals form 4 isosceles triangles Because a rectangle is a parallelogram: P1) exactly two pairs of parallel sides P2) opposite sides are parallel P3) opposite sides are congruent P4) both pairs of opposite angles are congruent P5) same-side interior angles are supplementary P6) diagonals bisect each other Because a rectangle is a quadrilateral: Q1) angles sum to 360 degrees

What are the properties of a rhombus?

RH1) all 4 sides are congruent RH2) diagonals are perpendicular RH3) diagonals bisect exactly two pairs of opposite angles Because a rhombus is a parallelogram: P1) exactly two pairs of parallel sides P2) opposite sides are parallel P3) opposite sides are congruent P4) both pairs of opposite angles are congruent P5) same-side interior angles are supplementary P6) diagonals bisect each other Because a rhombus is a quadrilateral: Q1) angles sum to 360 degrees

What are the properties of a square?

SQUARES HAVE NO UNIQUE PROPERTIES Because a square is a parallelogram: P1) exactly two pairs of parallel sides P2) opposite sides are parallel P3) opposite sides are congruent P4) both pairs of opposite angles are congruent P5) same-side interior angles are supplementary P6) diagonals bisect each other Because a square is a rectangle: RE1) all angles are right angles RE2) diagonals are congruent RE3) diagonals form 4 isosceles triangles Because a square is a rhombus: RH1) all 4 sides are congruent RH2) diagonals are perpendicular RH3) diagonals bisect exactly two pairs of opposite angles Because a square is a quadrilateral: Q1) angles sum to 360 degrees

If two angles or sides are congruent, what should you do?

Set them equal to each other. Then solve, if needed.

What are the properties of a trapezoid?

T1) exactly one pair of parallel sides T2) same-side interior angles on the same leg are supplementary T3) bases are parallel Because a trapezoid is a quadrilateral: Q1) angles sum to 360 degrees